A particle is projected vertically upwards from the surface of the earth (radius R) with a speed equal to one-fourth of escape velocity. The maximum height attained by it from the surface of the earth is
A
R5
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B
R10
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C
R15
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D
R20
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Solution
The correct option is CR15 Escape velocity, ve=√2gR v=√2gR4=√gR2√2
From conservation of energy 12mv2−GMmR=0−GMmR+h
Using g=GMR2 12mgR8− mg R=−gR2mR+h 116=1−RR+h 116=hR+h R+h=16h R=15h h=R15